Triple

T22965137
Position Surface form Disambiguated ID Type / Status
Subject Le Grand Crible dans la Théorie Analytique des Nombres E571018 entity
Predicate appliesMethod P859 FINISHED
Object large sieve
The large sieve is a powerful analytic number theory technique that provides upper bounds for the distribution of sequences in arithmetic progressions and related sieve problems.
E1563187 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: large sieve | Statement: [Le Grand Crible dans la Théorie Analytique des Nombres, appliesMethod, large sieve]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: large sieve
Context triple: [Le Grand Crible dans la Théorie Analytique des Nombres, appliesMethod, large sieve]
  • A. Selberg sieve
    The Selberg sieve is a powerful analytic number theory method developed by Atle Selberg for estimating the size of sets of integers filtered by divisibility conditions, particularly in the study of prime numbers.
  • B. Brun sieve
    The Brun sieve is a combinatorial method in analytic number theory, developed by Viggo Brun, used to estimate the distribution of prime numbers and almost-primes in various sequences.
  • C. Brun combinatorial sieve
    The Brun combinatorial sieve is a classical number-theoretic sieving method, developed by Viggo Brun, that uses combinatorial techniques to estimate the distribution of integers free of small prime factors and was historically applied to problems like twin primes.
  • D. Siegel–Walfisz theorem
    The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
  • E. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: large sieve
Triple: [Le Grand Crible dans la Théorie Analytique des Nombres, appliesMethod, large sieve]
Generated description
The large sieve is a powerful analytic number theory technique that provides upper bounds for the distribution of sequences in arithmetic progressions and related sieve problems.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: large sieve
Target entity description: The large sieve is a powerful analytic number theory technique that provides upper bounds for the distribution of sequences in arithmetic progressions and related sieve problems.
  • A. Selberg sieve
    The Selberg sieve is a powerful analytic number theory method developed by Atle Selberg for estimating the size of sets of integers filtered by divisibility conditions, particularly in the study of prime numbers.
  • B. Brun sieve
    The Brun sieve is a combinatorial method in analytic number theory, developed by Viggo Brun, used to estimate the distribution of prime numbers and almost-primes in various sequences.
  • C. Brun combinatorial sieve
    The Brun combinatorial sieve is a classical number-theoretic sieving method, developed by Viggo Brun, that uses combinatorial techniques to estimate the distribution of integers free of small prime factors and was historically applied to problems like twin primes.
  • D. Siegel–Walfisz theorem
    The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
  • E. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69e245b2c6548190a0e4c7f2f7df2d48 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f181f763688190aab8f444a1a71577 completed April 29, 2026, 3:58 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0bca22caa88190889e965c78477a96 completed May 19, 2026, 2:25 a.m.
NEDg Description generation batch_6a0bcb1904c88190ac32e5709bc95858 completed May 19, 2026, 2:29 a.m.
NED2 Entity disambiguation (via description) batch_6a0bcbb8793881909621b16c9ad51cbb completed May 19, 2026, 2:32 a.m.
Created at: April 17, 2026, 3:47 p.m.